To gain a qualitative understanding of kinematics and how the qualitative nature of position andvelocity versus time graphs relates to the equations of kinematics.In this problem, you will explore kinematics using an applet that simulates a car moving under constant acceleration.When you openthe applet, you will see three sliders that allow you to adjust the initial position , the initial velocity ,and the acceleration . Set the initial position to 0 , the initial velocity to and the acceleration to 5 .Run the simulation. Notice that, as the movie proceeds, pictures of the car remain at certain points. Once the simulationis over, these pictures form a motion diagram--a representation of motion consisting of pictures taken at equal timeintervals during the motion. In this case, the interval between pictures is one second.Below the movie, the position of the car as a function of time is graphed in green. Run the simulation several times,paying attention to how the graph and the motion diagram/movie of the car's motion relate to each other.

Part A

Which of the following describe the relationship between the motion diagram/movie and the graph?

Check all that apply.

ANSWER:When the slope of the graph is close to zero, the pictures in the motion diagram are close together.When the slope of the graph is steep, the car is moving quickly.When the slope of the graph is positive, the car is to the right of its starting position.When the

x

position on the graph is negative, the car moves backward. When the

x

position on thegraph is positive, the car moves forward.When the

x

position on the graph is negative, the car moves slowly. When the

x

position on thegraph is positive, the car moves quickly.When the

x

position on the graph is negative, the car is to the left of its starting position. When the

x

position on the graph is positive, the car is to the right of its starting position.

All attempts used; correct answer displayed

Notice that the first and second options are always true, regardless of the values of , , and . The last option,however, is only true when . Frequently, you will be able to pick your coordinate system. In such cases,making is often a good choice.

Run the simulation, paying close attention to the graph of position. Press reset and change the value of . Runthe simulation again, noting any changes in the graph. How does varying affect the graph of position?

ANSWER:Increasing increases the width of the graph, whereas decreasing decreases the width.Increasing shifts the graph to the right, whereas decreasing it shifts the graph to the left.Increasing shifts the graph to the left, whereas decreasing it shifts the graph to the right.Increasing shifts the graph upward, whereas decreasing it shifts the graph downward.Increasing shifts the graph downward, whereas decreasing it shifts the graph upward.Changing does not affect the graph.

Correct

Part C

Now, run the simulation with different values of , but don't use any positive values. Note any changes in the graph.How does varying affect the graph of position?

Choose the best answer.

ANSWER:Increasing increases the width of the graph, whereas decreasing decreases the width.Increasing shifts the graph to the right and upward, whereas decreasing it shifts the graph tothe left and downward.Increasing shifts the graph to the left and upward, whereas decreasing it shifts the graph tothe right and downward.Increasing shifts the graph to the right and downward, whereas decreasing it shifts the graphto the left and upward.Increasing shifts the graph to the left and downward, whereas decreasing it shifts the graphto the right and upward.Changing does not affect the graph.

Correct

This behavior may be a bit difficult to understand by just looking at the equation for position vs. time that you knowfrom kinematics. If you complete the square to get the equation into standard form for a parabola, this should becomemore apparent.Now that you've seen how affects the graph, run the simulation with a few different values of acceleration. Youshould see that increasing the acceleration decreases the width of the graph and decreasing the acceleration increasesthe width. (Decreasing the acceleration below 0 makes the parabola open downward instead of upward.)

Enter the equation for position as a function of time. Before submitting your answer, check that it is consistent withthe qualities of the graph that you have identified. For instance, if you increase in the equation, would it move thegraph upward?

Now, openthis applet. This applet looks like the previous applet, but when you run the simulation, you will now get graphsof both position and velocity. Run the simulation several times with different values of . How does changing affectthe graph of velocity?

ANSWER:Increasingincreases the slope of the graph, whereas decreasing decreases the slope.Increasing shifts the graph to the right, whereas decreasing it shifts the graph to the left.Increasing shifts the graph to the left, whereas decreasing it shifts the graph to the right.Increasing shifts the graph upward, whereas decreasing it shifts the graph downward.Increasing shifts the graph downward, whereas decreasing it shifts the graph upward.Changing does not affect the graph.

All attempts used; correct answer displayed

Part F

Run the simulation again, with the following settings: , , and . The units of time inthe graph are seconds. At what time is the velocity equal to zero?

Express your answer in seconds to the nearest integer.

ANSWER:

3

Correct

Notice that the position graph has a minimum when velocity equals zero. This should make sense to you. Since velocityis the derivative of position, position has a local minimum or maximum when velocity is zero.